# Coseparable Nonnegative Tensor Factorization With T-CUR Decomposition

arXiv: https://arxiv.org/abs/2401.16836 · HTML: https://mlsanity.com/paper/2401.16836/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation](https://mlsanity.com/paper/1310.7529/) (2013)
- [Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation](https://mlsanity.com/paper/2010.07422/) (2020)
- [A Fast Gradient Method for Nonnegative Sparse Regression with Self Dictionary](https://mlsanity.com/paper/1610.01349/) (2016)
- [A Tensor-Based Dictionary Learning Approach to Tomographic Image Reconstruction](https://mlsanity.com/paper/1506.04954/) (2015)
- [T-ADAF: Adaptive Data Augmentation Framework for Image Classification Network based on Tensor T-product Operator](https://mlsanity.com/paper/2306.04240/) (2023)

## Built on by (most cited first, 1 of 1)

- [Property Inheritance for Subtensors in Tensor Train Decompositions](https://mlsanity.com/paper/2504.11396/) (2025)

## Abstract (arXiv)

Nonnegative Matrix Factorization (NMF) is an important unsupervised learning method to extract meaningful features from data. To address the NMF problem within a polynomial time framework, researchers have introduced a separability assumption, which has recently evolved into the concept of coseparability. This advancement offers a more efficient core representation for the original data. However, in the real world, the data is more natural to be represented as a multi-dimensional array, such as images or videos. The NMF's application to high-dimensional data involves vectorization, which risks losing essential multi-dimensional correlations. To retain these inherent correlations in the data, we turn to tensors (multidimensional arrays) and leverage the tensor t-product. This approach extends the coseparable NMF to the tensor setting, creating what we term coseparable Nonnegative Tensor Factorization (NTF). In this work, we provide an alternating index selection method to select the coseparable core. Furthermore, we validate the t-CUR sampling theory and integrate it with the tensor Discrete Empirical Interpolation Method (t-DEIM) to introduce an alternative, randomized index selection process. These methods have been tested on both synthetic and facial analysis datasets. The results demonstrate the efficiency of coseparable NTF when compared to coseparable NMF.